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**Two objects of masses m1 and m2 have the same size are dropped simultaneously from heights h1 and h2 respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if**

**(i) one of the objects is hollow and the other one is solid and**

**(ii) both of them are hollow, size remaining the same in each case. Give reason.**

Answer:

h1 = 12 gt21

h2 = 12gt22

as x = ot1t2 2 = √h1/h2

As the acceleration remains the same, the ratio between two objects remains the same. In this case, acceleration does not depend upon mass and size.

"hello everyone welcome to leader
learning
i am good preet your science tutor
today's question is two objects of
masses
m1 and m2 have the same
size are dropped simultaneously from the
heights
h1 and h2 respectively
find out the ratio of time they would
take in reaching the ground
will this ratio remain same if
first one of the object is hollow
and the other one is solid second
both of them are hollow size remaining
the same
in each case give reasons so here
in the question two objects have been
given
but they are of same size and
drop from the height h1 and h2
you have to calculate the ratio of time
they would take in reaching the ground
so let's start our answer
see here we'll apply
the equation of motion that is second
equation of motion
h is equals to u t plus
half gt square
this we will apply here for finding out
the ratio of time
since the initial velocities are zero
here
okay because it is under the gravity
so u will be equals to zero
okay so the ratio equation will be
h is equals to half of
gt square now we'll apply this equation
for
both the masses for m1
and for m2
okay m1 and h1 height and for m2 and
h2 height so here h1 will be equals to
half of g t1 square
and this will h2 will be equals to half
of
g t2 square so this equations you will
get
now for the ratio you will compare the
formulas
okay we need t1 and t2
so we'll write t1 square upon 2 square
is equals to 2 h 1
upon g divided by
2 h 2 upon g
g will be cancelled by g this and 2
we cancel and you will get the ratio as
t 1 upon t 2 is equals to
under root of h 1
upon under root of h2
okay so
you will get the ratio t1 is 2 t2
will be under root h1
is to under root h2
this will be the ratio of time
now they have been asking that two
situations have been given
in one of the object is hollow and the
other one is solid
and in second situation both of them are
hollow but
in both the cases one and two size
remains the same
so due to all this
the conditions given acceleration
due to gravity
is same in both the cases
so the ratio
will also be same
because acceleration due to gravity it
does not depend on
mass and size of the objects
clear for more such videos
please subscribe leaderlearning and for
any doubts
drop a comment thank you"

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